We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. The key result is that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value T_c. At the same time, it can be also proven that at high enough T the conductivity is finite. These two statements imply that the system undergoes a finite temperature metal-insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. As a result, in the insulating phase electron-electron interaction alone is unable to cause the relaxation and establish the thermal equilibrium.
In the presence of a (weak) electron-phonon interaction conductivity becomes finite even in the insulating phase, so the transition is smeared into a crossover. Nevertherless, it still can qualitatively affect the nonlinear conduction, thus giving a possibility of its experimental observation. |